There are mixed opinions about stretching before vs after workouts. Most of the argument against pre-workout stretching is that the muscles aren't warmed up, increasing the risk for a pulled muscle. But that's not the case here, so you should be okay with stretching in between from a physical perspective. I have read some arguments against excessive stretching prior to weights due to possible injuries (muscles can be overstretched as well), but from what you're describing, that does not seem to be the case. (This applies more to serious flexabilty type stetching followed by major high intensity weight lifting).

The other thing that you are doing with the cool down is lowering your heart rate. Again, there's nothing wrong with that, although there are people who prefer to try to keep their heart rate up through an entire workout.

Ultimately, you should be fine doing the cool down either before or after you do the weight training.